This was the question posted to the Travel Talk column of the Washington Post. The answer man for that question mentioned that the couple could use the train and get off at various stops to see different sights during that 7 hours.
I would also have suggested to look into booking a tour guide. One that will meet you at the airport, hopefully with their own transport. Make a list of the things that you would like to see, if only to drive by. Then make a list of things that you want to tour. And pick a few out of each list. Assume that you will be back.
I would pick the Eiffel Tower to visit. But you may say - I've heard that the lines to go up are long. True, but if you are in reasonable health consider taking the stairs. The line is usually shorter there, the stairs are wide - plenty of room for stopping and resting while taking in the view and it only goes to the second story - about 600 or so steps. That is plenty high enough to get a great view of the city in all directions and take some photos. Plus, going down is easier :-).
Also, once you have your list of things to visit make sure that they are open on the day you plan to tour the city. Various sights are closed at least one day during the week. You don't want to waste time and energy.